Primal Spectral Distance

Here is a heatmap of the spectral distances between the Primal Classification Hypegraphs (or Model 1 Hypergraphs), where vertices are cells and hyperedges are cell fates. The hyeprgraphs have been sorted in the heatmap such the species tested on is grouped together. It is clear to see, that all hypergraphs tested on the same species have low spectral distance between them, except for Human 3 who’s spectral distance is much closer to mice than it is to humans.

Heatmap

UMAP Representation of Spectral Projection

Dual Spectral Distance

Here is a heatmap of the spectral distances between the Dual Classification Hypegraphs (or Model 2 Hypergraphs), where vertices are cell fates and hyperedges are cells. It is harder to immediately analyse these resluts by inspection. There is a definite pattern to the data with respect to the species the classifiers were tested and trained on. It is interesting to note that the spectral distances between all hypergraphs where the classifier was both tested and trained on the same species is low. Oimilarly to the primal case, the pattern in the data is broken by Human 3. The hypergraphs of classifiers trained on Human 3 but then tested on mice has a starkly different heatmap to other similar classifiers.

Heatmap

A Statisic

Balanced Accuracy Compared to Spectral Distance From the Disconnected Hypergraph

Spectral Distance From the Disconnected Hypergraph as a Measure of Confidence

The spectral distance from the disconnected hypergraph might be able to be used as a measure of confidence of a set of classifications. The disconnected hyeprgraph (the hypergraph where all hyperedges are a loop around one vertex) in the context of hypergraphs created using ML softmax output, would represent a classifier that was completely confident with every classification. Therefore, the greater the spectral distance between a given hypergraph and the disconnected hypergraph the less structural similarities there are between them and therefore the less likely it is to represent stronlgy confident classifications.

There is an apparent pattern in the data that the lower the balanced accuracy, the higher the spectral distance (the less confident the predictions are). It is noticable that there are two distinct trends, one for the classifications tested on mice and one for the classifications tested on humans.

Average Balanced Accuracy of Intraspecies Classifications

Average Spectral Distance From the Disconnected Hypergraph of Intraspecies Classifications

1.51

Average Balanced Accuracy of Interspecies Classifications

Average Spectral Distance From the Disconnected Hypergraph of Interspecies Classifications

4.88